2020

Scientific Articles

unige:133524	A New Class of Uniformly Accurate Numerical Schemes for Highly Oscillatory Evolution Equations	Chartier, Philippe; Lemou, Mohammed; Méhats, Florian; Vilmart, Gilles;
unige:123872	Exotic aromatic B-series for the study of long time integrators for a class of ergodic SDEs	Laurent, Adrien; Vilmart, Gilles;
unige:133525	Multirevolution Integrators for Differential Equations with Fast Stochastic Oscillations	Laurent, Adrien; Vilmart, Gilles;
unige:142618	Strang Splitting Method for Semilinear Parabolic Problems With Inhomogeneous Boundary Conditions: A Correction Based on the Flow of the Nonlinearity	Bertoli, Guillaume Balthazar; Vilmart, Gilles;

Preprints

unige:136314

Drift-preserving numerical integrators for stochastic Poisson systems

Cohen, David; Vilmart, Gilles;

Thesis supervisions

unige:145482

Explicit Stabilized Methods for Stiff Stochastic Differential Equations and Stiff Optimal Control Problems

Almuslimani, Ibrahim;

2019

Scientific Articles

unige:118369	Accelerated convergence to equilibrium and reduced asymptotic variance for Langevin dynamics using Stratonovich perturbations	Abdulle, Assyr; Pavliotis, Grigorios A.; Vilmart, Gilles;
unige:118370	Highly oscillatory problems with time-dependent vanishing frequency	Chartier, Philippe; Lemou, Mohammed; Méhats, Florian; Vilmart, Gilles;

2018

Scientific Articles

unige:105971

Optimal explicit stabilized integrator of weak order one for stiff and ergodic stochastic differential equations

Abdulle, Assyr; Almuslimani, Ibrahim; Vilmart, Gilles;

2017

Scientific Articles

unige:102841	Computing the long term evolution of the solar system with geometric numerical integrators	Fiorelli, Shaula; Vilmart, Gilles;
unige:96975	Fast Langevin based algorithm for MCMC in high dimensions	Durmus, Alain; Roberts, Gareth O.; Vilmart, Gilles; Zygalakis, Konstantinos C.;

Master's thesis supervisions

unige:121404

Splitting methods for the Schrödinger equation with absorbing boundary conditions

Bertoli, Guillaume Balthazar;

2016

Scientific Articles

unige:80936	Asymptotic Preserving numerical schemes for multiscale parabolic problems	Crouseilles, Nicolas; Lemou, Mohammed; Vilmart, Gilles;
unige:86147	High Order Integrator for Sampling the Invariant Distribution of a Class of Parabolic Stochastic PDEs with Additive Space-Time Noise	Bréhier, Charles-Edouard; Vilmart, Gilles;

2015

Scientific Articles

unige:79120	Linearized numerical homogenization method for nonlinear monotone parabolic multiscale problems	Abdulle, Assyr; Huber, Martin; Vilmart, Gilles;
unige:41848	Long time accuracy of Lie-Trotter splitting methods for Langevin dynamics	Abdulle, Assyr; Vilmart, Gilles; Zygalakis, Konstantinos C.;
unige:79277	Postprocessed Integrators for the High Order Integration of Ergodic SDEs	Vilmart, Gilles;
unige:41845	Reduced basis finite element heterogeneous multiscale method for quasilinear elliptic homogenization problems	Abdulle, Assyr; Bai, Yun; Vilmart, Gilles;

Contributions à un dictionnaire / une encyclopédie

unige:79453

Rigid body dynamics

Vilmart, Gilles;

2014

Scientific Articles

unige:41954	An offline-online homogenization strategy to solve quasilinear two-scale problems at the cost of one-scale problems	Abdulle, Assyr; Bai, Yun; Vilmart, Gilles;
unige:41959	Analysis of the finite element heterogeneous multiscale method for quasilinear elliptic homogenization problems	Abdulle, Assyr; Vilmart, Gilles;
unige:41847	High Order Numerical Approximation of the Invariant Measure of Ergodic SDEs	Abdulle, Assyr; Vilmart, Gilles; Zygalakis, Konstantinos C.;
unige:41957	Multi-revolution composition methods for highly oscillatory differential equations	Chartier, Philippe; Makazaga, Joseba; Murua, Ander; Vilmart, Gilles;
unige:41846	Weak Second Order Multirevolution Composition Methods for Highly Oscillatory Stochastic Differential Equations with Additive or Multiplicative Noise	Vilmart, Gilles;

2013

Scientific Articles

unige:41955	Mean-square A-stable diagonally drift-implicit integrators of weak second order for stiff Itô stochastic differential equations	Abdulle, Assyr; Vilmart, Gilles; Zygalakis, Konstantinos C.;
unige:41948	PIROCK: A swiss-knife partitioned implicit–explicit orthogonal Runge–Kutta Chebyshev integrator for stiff diffusion–advection–reaction problems with or without noise	Abdulle, Assyr; Vilmart, Gilles;
unige:41956	Weak Second Order Explicit Stabilized Methods for Stiff Stochastic Differential Equations	Abdulle, Assyr; Vilmart, Gilles; Zygalakis, Konstantinos C.;

2012

Scientific Articles

unige:41958	A priori error estimates for finite element methods with numerical quadrature for nonmonotone nonlinear elliptic problems	Abdulle, Assyr; Vilmart, Gilles;
unige:41946	Coupling heterogeneous multiscale FEM with Runge-Kutta methods for parabolic homogenization problems: a fully discrete space-time analysis	Abdulle, Assyr; Vilmart, Gilles;
unige:41947	High Weak Order Methods for Stochastic Differential Equations Based on Modified Equations	Abdulle, Assyr; Cohen, David; Vilmart, Gilles; Zygalakis, Konstantinos C.;

2011

Scientific Articles

unige:41942

The effect of numerical integration in the finite element method for nonmonotone nonlinear elliptic problems with application to numerical homogenization methods

Abdulle, Assyr; Vilmart, Gilles;

2010

Scientific Articles

unige:12105

Algebraic structures of B-series

Chartier, Philippe; Hairer, Ernst; Vilmart, Gilles;

2009

Scientific Articles

unige:10685	Splitting methods with complex times for parabolic equations	Castella, F.; Chartier, P.; Descombes, S.; Vilmart, Gilles;
unige:5210	The role of symplectic integrators in optimal control	Chyba, Monique; Hairer, Ernst; Vilmart, Gilles;

2008

Scientific Articles

unige:42005

Reducing round-off errors in rigid body dynamics

Vilmart, Gilles;

Doctoral Thesis

unige:1337

Étude d'intégrateurs géométriques pour des équations différentielles

Vilmart, Gilles;

2007

Scientific Articles

unige:12055	Modified differential equations	Chartier, Philippe; Hairer, Ernst; Vilmart, Gilles;
unige:9712	Numerical integrators based on modified differential equations	Chartier, Philippe; Hairer, Ernst; Vilmart, Gilles;

2006

Scientific Articles

unige:12110

Preprocessed Discrete Moser-Veselov algorithm for the full dynamics of the rigid body

Hairer, Ernst; Vilmart, Gilles;